在统计学中, 研究随机变量之间的相关性是重要的课题之一. Copula 模型是刻画变量间相关性的常用方法, 它通过一个联结函数将两个或者多个边际分布结合在一起, 从而给出多维变量的联合分布. Copula 模型中的联结参数通常假设为一个常数. 然而, 在实际问题中, 数据间的相关性可能会随着时间或其他观测变量的改变而改变. 为了研究数据相关性的动态变化, 本文给出一类变联结参数的 Copula 模型. 该模型在一定程度上提高了Copula 模型的灵活性, 为研究相关关系提供了新的思路. 本文主要研究边际分布服从加法危险率模型的二元生存数据的变联结参数的 Copula 模型, 分别考虑了边际分布为变系数和常系数加法危险率模型两种情况. 我们采用两阶段估计法给出联结参数的估计. 第一阶段, 对于时间相依系数的加法模型和常系数加法危险率模型, 我们分别使用Aalen (1989) 提出的最小二乘法和Lin和Ying (1994) 估计方程的方法, 给出加法模型参数的估计值, 进而得到边际生存函数的估计; 第二阶段, 将所得边际生存函数的估计带入局部伪似然函数中, 得到联结参数的局部估计量. 并且我们推导出所给联结参数估计量的相合性. 为了检验所提方法在有限样本下的表现, 论文的第五章给出了相应的数值模拟.

The study of dependence between random variables is important in statistics. Copula model is a popular method to model dependence between variables. A multivariate distribution can be fully characterized by its marginal distributions and a copula function. We usually assume that the association parameter is fixed. But in practice, the strength of dependence between random variables may vary according to the values of time or other covariates. We propose inference for this type of variation using varying-association parameter Copula model. This model improves the flexibility of Copula model, and provides a new idea for studying the dependence. This paper mainly studies the varying-association parameter Copula model of bivariate survival data, and its marginal hazard function is time-varying additive hazard model and additive hazard model. We propose the two-stages estimate method to estimate the association parameter. In the first stage, we estimate the parameter of the additive model by using the least square method proposed by Aalen (1989) and the method of Lin and Ying (1994) respectively, and then obtain the estimate of marginal survival distribution. In the second stage, by replacing the estimates of marginal survival distribution in local pseudo-likelihood, we can get the local estimate of the association parameter. We derive the consistency of the resulting local pseudo-likelihood estimator. In order to investigate the finite-sample performance of this method, we show simulation studies in chapter 5.